CSC 371
Homework 3

Assigned Sept. 29, due Oct. 14

Problems from Chapter 3 (arithmetic)

• Exercises 3.2.1 through 3.2.6 on integer arithmetic. (Use row a examples. For exercises 3.2.1-3, there's a mistake in the textbook: the sign bits are all zero, so “treating the numbers as signed” makes no difference. Since this is boring, treat the numbers as 15-bit rather than 16-bit.)
• Exercises 3.5.1 through 3.5.3 on the speed of different approaches to multiplication. Use row a numbers.
• Exercises 3.10.1 through 3.10.3 on interpreting bit patterns (use row b numbers).
• Exercises 3.11.1 and 3.11.2 on floating-point formats (use row b numbers). Note that where the textbook says "excess-56 format", this is a typo: it means excess-16. According to Wikipedia, the official half-precision floating-point format uses excess-15, with exponent fields 000000 and 111111 being treated specially, but I want you to answer the question for a simplified representation in which 111111 is not treated specially, and the bias is 16.
• Exercises 3.13.1 through 3.13.3 on associativity (use row a)

Logic design problem

Use LogiSim to build and test a circuit that acts as a three-bit integer ALU (i.e. it operates on three-bit signed integers, in two's-complement notation, so the range of possible values is -4 to +3).
Correction: I originally wrote that the range is -8 to +7. A student helpfully pointed out that that takes four bits. I apologize for the error.
It should be able to perform five two-input operations: AND, OR, ADD, SUB, and SLT, each producing a three-bit result. Since there are five operations, you'll need 3 bits of "opcode"; you may decide for yourself which 3-bit pattern corresponds to which operation. Don't worry about detecting arithmetic overflow.

You may use LogiSim's built-in AND, OR, NOT, NAND, NOR, XOR, and MUX gates, in single-output form; you may not use the built-in arithmetic gadgets, nor LogiSim's multi-output gadgets that stand for a bunch of components in parallel. You may want to build some simple gadgets (like a full-adder) of your own and use them as black-boxes in your main circuit.